Analysis and estimation of error constants for P0and P 1 interpolations over triangular finite elements

Xuefeng Liu, Fumio Kikuchi

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We give some fundamental results on the error constants for the piecewise constant interpolation function and the piecewise linear one over triangles. For the piecewise linear one, we mainly analyze the conforming case, but the present results also appear to be available for the non-conforming case. We obtain explicit relations for the upper bounds of the constants, and analyze dependence of such constants on the geometric parameters of triangles. In particular, we explicitly determine some special constants including the BabuškaAziz constant, which plays an essential role in the interpolation error estimation of the linear triangular finite element. The obtained results are expected to be widely used for a priori and a posteriori error estimations in adaptive computation and numerical verification of numerical solutions based on the triangular finite elements. We also give some numerical results for the error constants and for a posteriori estimates of some eigenvalues related to the error constants.

Original languageEnglish
Pages (from-to)27-78
Number of pages52
JournalJournal of Mathematical Sciences
Volume17
Issue number1
Publication statusPublished - 2010

Fingerprint

Triangular
Interpolate
Finite Element
Piecewise Linear
Triangle
Numerical Verification
A Posteriori Estimates
A Posteriori Error Estimation
Interpolation Error
Interpolation Function
Constant function
Error Estimation
Numerical Solution
Upper bound
Eigenvalue
Numerical Results

Keywords

  • Error estimates
  • FEM
  • Interpolation error constants
  • Triangular finite elements

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Analysis and estimation of error constants for P0and P 1 interpolations over triangular finite elements. / Liu, Xuefeng; Kikuchi, Fumio.

In: Journal of Mathematical Sciences, Vol. 17, No. 1, 2010, p. 27-78.

Research output: Contribution to journalArticle

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